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Thread: Movement of the field

  1. #1
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    Movement of the field

    Find the movement of the field
    $\displaystyle F(x,y) = (x^2-y)i + (x-y^2)j$

    arrond the curve $\displaystyle \alpha$ which is the boundary of the region in 1 quedrant understood by coordinated axes and the circle $\displaystyle x^2+y^2=16$

    My solution

    $\displaystyle \int_0^{\frac{ \pi}{2}} (-64cos^2tsint +16sen^2t+16cos^2t-64sen^2tcost)dt = 8 \pi$

    Correct ?
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  2. #2
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    I figured again and got:

    $\displaystyle 8 \pi \frac{128}{3}$
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  3. #3
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    Quote Originally Posted by Apprentice123 View Post
    Find the movement of the field
    $\displaystyle F(x,y) = (x^2-y)i + (x-y^2)j$

    arrond the curve $\displaystyle \alpha$ which is the boundary of the region in 1 quedrant understood by coordinated axes and the circle $\displaystyle x^2+y^2=16$

    My solution

    $\displaystyle \int_0^{\frac{ \pi}{2}} (-64cos^2tsint +16sen^2t+16cos^2t-64sen^2tcost)dt = 8 \pi$

    Correct ?

    For this one you would want to use Greens' theorem:

    $\displaystyle \iint_D 1-(-1)dA=2 \iint_D dA=2 \frac{1}{4}\pi (4)^2=8\pi$
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  4. #4
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    Thank you
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